Translation:Please put the bag here.
It would be implied by context.
If I went to the airport and the check-in Clerk sais to me, while pointing beside them “かばんをここにおいてください。” Then I would think “Please put your bag here.” Because they were talking to me.
If I went onto a train in Japan that had a compartment for luggage, the sign could say “かばんをおいてください。” Which could then say “Please leave bags here.”
Japanese is a very contextual language.
I agree Japanese is very contextual. This sentence COULD mean "my bag", "your bag", "his/her bag", or "the bag" because the possession of the bag is not identified in the sentence.
If my neighbor was helping my carry my groceries to my apartment, I would say "カバンをここにおいてください" to mean " Please place MY bag here".
If a taxi drive was unloading luggage from the trunk for my wife and I, and he pulled out my wife's bag, I would say "カバンをここにおいてください" to mean "Please place HER bag here."
Without any indication of the context (and there is no indication of context in the text カバンをここにおいてください.) I think the best translation would be "Please place THE bag here" because "the" bag could be mine, yours, or his/hers. Any of the other translations forces the learner to make an assumption of context which is not present in the source text.